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Found 16 papers, 3 papers with code
Position Paper: Challenges and Opportunities in Topological Deep Learning
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models.
Current Topological and Machine Learning Applications for Bias Detection in Text
Institutional bias can impact patient outcomes, educational attainment, and legal system navigation.
Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach
We begin by introducing three practical properties associated with the notion of robustness in hierarchical clustering: linear scale preservation, stability, and excisiveness.
Topological Deep Learning
This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods.
Evaluating the Disentanglement of Deep Generative Models through Manifold Topology
Learning disentangled representations is regarded as a fundamental task for improving the generalization, robustness, and interpretability of generative models.
A Topology Layer for Machine Learning
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning.
Topological Approaches to Deep Learning
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform.
Exposition and Interpretation of the Topology of Neural Networks
We use topological data analysis to show that the information encoded in the weights of a CNN can be organized in terms of a topological data model and demonstrate how such information can be interpreted and utilized.
Fibres of Failure: Classifying errors in predictive processes
We describe Fibres of Failure (FiFa), a method to classify failure modes of predictive processes using the Mapper algorithm from Topological Data Analysis.
Hierarchical Clustering of Asymmetric Networks
This paper considers networks where relationships between nodes are represented by directed dissimilarities.
Admissible Hierarchical Clustering Methods and Algorithms for Asymmetric Networks
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation.
Excisive Hierarchical Clustering Methods for Network Data
We introduce two practical properties of hierarchical clustering methods for (possibly asymmetric) network data: excisiveness and linear scale preservation.
Hierarchical Quasi-Clustering Methods for Asymmetric Networks
This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data.
The Ring of Algebraic Functions on Persistence Bar Codes
We study the ring of algebraic functions on the space of persistence barcodes, with applications to pattern recognition.
Rings and Algebras 13Pxx, 68T10
Axiomatic Construction of Hierarchical Clustering in Asymmetric Networks
Our construction of hierarchical clustering methods is based on defining admissible methods to be those methods that abide by the axioms of value - nodes in a network with two nodes are clustered together at the maximum of the two dissimilarities between them - and transformation - when dissimilarities are reduced, the network may become more clustered but not less.
Classifying Clustering Schemes
In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality.
